The Paradox of Infinity

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RuroumiKenshin

What is infinity? How can something infinite expand? Once and for all, how can we conclude that the universe is infinite? The fact that the universe is infinite may contradict brane theory. Consequently, could it be tenable to suggest that this brane is a subuniverse?
Of course, the idea of an infinite universe could just be based on the inifite boundary theory proposed by Stephen Hawking.
 
I feel it important, nay nessesary, to point out, right before this discussion begins that....

Infinity is NOT a number.

It is NOT a number.

Thank you. Please bear this in mind.
 
3,754
2
Majin, you should perhaps have posted this in the Philosophy Forum.

Infinity is the concept of something that goes on forever.

Something infinite cannot expand (IMO).

We can never conclude that the universe is infinite, beyond question.

No, branes are not "sub-universes". Branes are mathematical additions of dimensions (AFAIK).
 
167
1
Without meaning to be insulting, but how can someone not yet able to manipulate equations claim to be able to reason about brane theory?
 

drag

Science Advisor
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What's all this talk about infinity being
paradoxical, all the time? What's so paradoxical
about it ? (I guess this should indeed be in the
philosophy forum.)

What's paradoxical about expanding infinity ?

Live long and prosper.
 

RuroumiKenshin

I knew I should've put this is in the philosophy forum! *slaps head* tsk, tsk.

Anyhow, infinity is paradoxical because, as Mentat pointed out, something infinite is unable to expand. It goes on, and on, forever so how can something infinite expand?
 

RuroumiKenshin

Originally posted by plus
Without meaning to be insulting, but how can someone not yet able to manipulate equations claim to be able to reason about brane theory?
I'm working on it. Any how, I love doing math, because its just like a logic problem, and I love those too.

plus, what you said was not insulting. The truth is never,AFAIK, insulting.
 

drag

Science Advisor
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Greetings !
Originally posted by MajinVegeta
Anyhow, infinity is paradoxical because, as
Mentat pointed out, something infinite is
unable to expand. It goes on, and on, forever
so how can something infinite expand?
Well, if it's only spacial expansion for example
then the distances between all objects will
simply grow.

Do understand me people - I'm not, at the moment,
denying the concept of real infinity as having
its own paradox of some kind, but I have yet
to see any clear fomalization of such a paradox.

Live long and prosper.
 
3,754
2
Originally posted by plus
Without meaning to be insulting, but how can someone not yet able to manipulate equations claim to be able to reason about brane theory?
What/who are you talking about?
 
3,754
2
Originally posted by drag
Greetings !

Well, if it's only spacial expansion for example
then the distances between all objects will
simply grow.
No, no, I was talking about the idea that the spacial dimensions themselves are expanding, not just that things are getting farther apart.
 
167
1
Something infinite can expand.

Consider the set of the numbers A = {1, 2, 3, ......}, and now consider the set of A and 1/2, so it is B := {1/2, 1, 2, 3, 4, 5, 6, 7, ..}.

Then there is one number in B which is not in A. This could be said to be an expansion of A.

This I believe is a counterexample to one of Mentat's ascertations:

'Something infinite cannot expand',

although he needs say more precisely what he means by this.
 

positron98

This infinity talk remindes me of cardinality, countable, and uncountable sets. It's a really cool topic in mathematical analysis. In a sense, not all infinities are equal, i.e., not all sets with infinite number of elements can be enumerated. For instance, the interval (0,1) or any finite interval on the real line is larger than the set of all integers.
 

drag

Science Advisor
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Greetings !
Originally posted by Mentat
No, no, I was talking about the idea that
the spacial dimensions themselves are
expanding, not just that things are
getting farther apart.
That IS what I meant. Plus gives an appropriate
example here.

For example, suppose that you draw coordinates
and assign a number to every area of specific
size. Then multiply your infinite set of areas
by 2 and you'll see that the amount of areas
is now twice the previous amount - between say
your house and the nearest store.

It may be conceptually difficult, but if you
consider that space is infinite you don't have
to worry about what's outside at all - simply
don't bother yourself with that thought.
(I must note that I find it difficult, at this time,
to think of a more solid formalization of this idea,
so perhaps there is a fundumental mistake of some
kind in this line of reasoning.)

Live long and prosper.
 
3,754
2
Alright, let me explain: I am not talking about mathematical infinities. I know that there can be more than one infinity, in maths, and that there can be "bigger" infinities. However, I'm talking about space itself. If you take a space that is infinite (as in, having no end), how could you possibly add more space to this? Even if you could, (though I don't think you could) your result would be the same as before (infinity), and thus you haven't made it any bigger at all.
 

drag

Science Advisor
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Well, I wasn't talking about math, just using
it as an example. The question is - what's the
difference ? Is there any ? And why ?

Live long and prosper.
 

RuroumiKenshin

If it is already infinite, it can't quite get bigger. Infinity is having no end, eternal. Infinity describes endlessness in the whole so you can't add anything to it.
 

dav2008

Gold Member
608
1
ok ok ..right...BUT ..did you see that example?

Take all even numbers...you would agree that there are an infinite amount of them....But you can always add an odd number to that set of inifinite numbers...just like "plus" said...

Its more mathematical in that sense...not physical..
 

RuroumiKenshin

Yes, I know that in mathematics infinity can be added with another infinity and the sort. BUT, my question is in the physical sense. We can't run away from the physical world.
 

Locutus

Originally posted by MajinVegeta
Yes, I know that in mathematics infinity can be added with another infinity and the sort. BUT, my question is in the physical sense. We can't run away from the physical world.
I believe that what separates the mathematical universe from the physical universe is practicality. Practicality tells us that in order to exist, the universe must have physical laws. These laws (speed of light, for example) impose finite barriers in an attempt to give order to the universe. Even though these laws do prevent many physical infinities (max speed, min temp, etc), the fact that the universe is in constant motion creates many new infinities.

A common infinity is the coastline of great britain. It is impossible to obtain an exact answer for this, for to do so one must measure at increments infinitely less than planck length, which would require so much energy as to warp space enough to disrupt their results. Not to mention the uncertainty principle...

This is not to say that Britain does not have a definite coastline at a specific increment of time. It does, yet practicality (that word again) prevents us from saying so, because WE cannot obtain this measurement. The physical universe has a human element to it that the mathematical universe lacks. Einstein said that "Only two things are infinite: the universe and human stupidity, and I'm not sure about the former." So perhaps the universe is finite, and humans are so infinitely stupid that they cannot comprehend this.

Perhaps this thread belongs in the "philosophy" forum, but oh well.
 

RuroumiKenshin

Yes, maybe I should ask a moderator to move this thread to philosophy.

Anyway, you bring up an excellent point that has been neglected. Although, it occurs to me that the concept of human stupidity being the obstacle of our understanding of the universe seems be undefined. I came upon this conclusion on the premise that everything is relative. If you were traveling at c, the external world would become blue shifted. But to an external observer, you are the one who is blue shifted. So, you, and the observer are both correct for the whole matter is anisotropic and each of you has the right to your observations. Now, from our perspective, the universe is infinite. Possibly, to an "external" observer, the universe, perhaps, is not infinite. I doubt stupidity has anything to do with the matter.
 

dr-dock

if i may say what i think of infinity?

infinity is the only other singular point as zero is in respect to positive and negative.make XOY system.it's flat surface/plane with 4 infinity points (2 on each axis).now try to do this:
shift x and y for infinity.you'll get that they both begin with -0 and end with +0 while there is only one infinity in the center.i think that XOY should transform into sphere with radius inf/2 where zero and inf are diametricaly oposite.
 

RuroumiKenshin

To make my point defintely established:

THIS THREAD IS MAINLY QUESTIONING THE PHYSICAL PARADOXES OF INFINITY. NOT MATHEMATICAL PROSPECTS.
 

drag

Science Advisor
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Originally posted by MajinVegeta
THIS THREAD IS MAINLY
QUESTIONING THE PHYSICAL PARADOXES OF INFINITY.
NOT MATHEMATICAL PROSPECTS.
Indeed. But, should there be a fundumental
difference ? And why ?
(I adressed this above, I believe.)

Live long and prosper.
 

Stormy

I want to expand on the definition of infinity (no pun intended):

In my mind at least, infinity is something that, not only goes on forever, but also has gone on for ever, well as far as the Physical definition goes (refering to the universe)
 
167
1
There is no need for such large writing.

Mathematics is used to describe the physical universe. Things which are infinite CAN get larger.

A physical example of something getting larger.

Consider the domain in which you are allowed to move in cylindrical coordinates.
Now suppose that at a time t, you are allowed to move in the range
0< theta < t, where theta is the angle in degrees and that there is no restriction on the vertical range or the horizontal distance.

Then up to t=360, although the domain is infinite, it is still expanding. This is not "just a mathematical infinity" it is a practical one, which I have described the only way possible, using mathematics.


NB I could have easily chosen the function so that it increased for ever, but chose this one as it is easier to see what is happening.

Surely you will see now!!!
 

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